Airfoil profile for a turbine blade

ABSTRACT

An airfoil profile for a turbine blade of a gas turbine is provided. The turbine blade may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

TECHNICAL FIELD

This application relates to airfoils for a gas turbine and more particularly to an airfoil profile for a turbine blade of a gas turbine.

BACKGROUND

Turbines are machines that obtain rotational force by impulsive or reaction force using a flow of a compressible fluid such as steam or gas, and include a steam turbine using steam, a gas turbine using high-temperature and high-pressure combustion gas, and so on.

The gas turbine includes a compressor, a combustor, and a turbine. The compressor includes an air inlet into which air is introduced, and a plurality of compressor vanes and a plurality of compressor blades which are alternately arranged in a compressor housing. The introduced air is compressed by the compressor vanes and the compressor blades while passing through an inside of the compressor.

The combustor mixes fuel with compressed air supplied from the compressor and combusts the mixture of the fuel and the compressed air to generate high-temperature and high-pressure combustion gas.

The turbine includes a plurality of turbine vanes and a plurality of turbine blades which are alternately arranged in a turbine housing. In addition, a rotor is arranged to pass through centers of the compressor, the combustor, the turbine, and an exhaust chamber.

The rotor is rotatably supported at both ends thereof by bearings. A plurality of disks are fixed to the rotor, and a plurality of blades are connected to each of the disks while a drive shaft of a generator is connected to an end of the exhaust chamber.

In the gas turbine, the air compressed by the compressor is mixed with fuel in a combustion chamber so that the mixture thereof is burned to generate high-temperature and high-pressure combustion gas, the generated combustion gas is supplied to the turbine, and the combustion gas generates a rotational force while passing through the turbine blades, thereby rotating the rotor.

In a gas turbine, many system requirements should be met at each stage of the gas turbine to meet design goals. The design goals may include overall improved efficiency and airfoil loading capability. For example, a turbine blade airfoil profile should achieve thermal and mechanical operating requirements for that particular stage. There is thus a desire for an improved turbine blade airfoil profile for use in a turbine and the like.

SUMMARY

Aspects of one or more exemplary embodiments provide a unique airfoil profile for the turbine blades of a turbine stage capable of enhancing aeromechanics and reducing thermal and mechanical stresses.

Additional aspects will be set forth in part in the description which follows and, in part, will become apparent from the description, or may be learned by practice of the exemplary embodiments.

According to an aspect of an exemplary embodiment, there is provided a turbine blade including: an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

The airfoil shape may lie within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

The airfoil shape may lie within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.

The airfoil shape may lie within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.

A height of the airfoil portion may be approximately 9 to 11 inches.

A height of the turbine blade may be approximately 16 to 18 inches.

The turbine blade may further include a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.

According to an aspect of another exemplary embodiment, there is provided a turbine including: a rotor disk configured to be rotatable and a plurality of turbine blades installed on the rotor disk, wherein each of the turbine blade may include an airfoil having a blade-shape extending from a platform to a tip shroud and including a leading edge, a trailing edge, a pressure side extending from the leading edge to the trailing edge, and a suction side extending from the leading edge to the trailing edge, and wherein the turbine blade may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

According to an aspect of another exemplary embodiment, there is provided a gas turbine including: a compressor configured to compress air; a combustor configured to mix compressed air supplied from the compressor with fuel for combustion; and a turbine including a plurality of turbine nozzles and a plurality of turbine blades rotated by combustion gas to generate power, wherein each of the turbine blades extending from a platform to a tip shroud and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, and wherein the turbine blade may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects will become more apparent from the following description of the exemplary embodiments with reference to the accompanying drawings, in which:

FIG. 1 is a partially cutaway perspective view illustrating a gas turbine according to an exemplary embodiment;

FIG. 2 is a cross-sectional view illustrating a schematic structure of the gas turbine of FIG. 1;

FIG. 3 is a schematic diagram of a turbine illustrating a second stage bucket airfoil according to an exemplary embodiment;

FIG. 4 is a perspective view of a turbine blade including an airfoil according to an exemplary embodiment;

FIG. 5 is an alternative perspective view of the turbine blade including an airfoil of FIG. 4; and

FIG. 6 is an airfoil shape including a thinned outboard section according to an exemplary embodiment.

DETAILED DESCRIPTION

Various modifications and various embodiments will be described below in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the disclosure. It should be understood, however, that the various embodiments are not for limiting the scope of the disclosure to the specific embodiment, but they should be interpreted to include all modifications, equivalents, and alternatives of the embodiments included within the spirit and scope disclosed herein.

Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings. Throughout the disclosure, like reference numerals refer to like parts throughout the various figures and exemplary embodiments. In certain embodiments, a detailed description of functions and configurations well known in the art may be omitted to avoid obscuring appreciation of the disclosure by a person of ordinary skill in the art. For the same reason, some components may be exaggerated, omitted, or schematically illustrated in the accompanying drawings.

FIG. 1 is a partially cutaway perspective view illustrating a gas turbine according to an exemplary embodiment. FIG. 2 is a cross-sectional view illustrating a schematic structure of the gas turbine of FIG. 1.

Referring to FIGS. 1 and 2, the gas turbine 1000 may include a compressor 1100, a combustor 1200, and a turbine 1300. Based on a flow direction of gas (e.g., compressed air or combustion gas), the compressor 1100 is disposed at an upstream side of the gas turbine 1000, and the turbine 1300 is disposed at a downstream side of the gas turbine 1000. The combustor 1200 is disposed between the compressor 1100 and the turbine 1300.

The compressor 1100 includes compressor vanes 1120 and compressor rotors in a compressor housing. The turbine 1300 includes turbine vanes 1320 and turbine rotors in a turbine housing. The compressor vanes 1120 and the compressor rotors are arranged in a multi-stage arrangement along the flow direction of compressed air. The turbine vanes 1320 and the turbine rotors are arranged in a multi-stage arrangement along the flow direction of combustion gas. The compressor 1100 is designed such that an internal space is gradually decreased in size from a front stage to a rear stage so that air drawn into the compressor 1100 can be compressed. On the contrary, the turbine 1300 is designed such that an internal space is gradually increased in size from a front stage to a rear stage so that combustion gas received from the combustor 1200 can expand.

A torque tube for transmitting a rotational torque generated by the turbine 1300 to the compressor 1100 is disposed between a compressor rotor that is located at the rearmost stage of the compressor 1100 and a turbine rotor that is located at the foremost stage of the turbine 1300. FIG. 2 illustrates a case in which the torque tube includes multiple torque tube disks arranged in a three-stage arrangement, but it is understood that this is only an example and other exemplary embodiments are not limited thereto. For example, the torque tube may include multiple torque tube disks arranged in an arrangement of equal to or greater than four stages or an arrangement of equal to or less than two stages.

Each of the compressor rotors includes a compressor rotor disk and a compressor blade 1110 fastened to the compressor disk. That is, the compressor 1100 includes a plurality of compressor rotor disks, and respective compressor rotor disks are coupled to each other by a tie rod to prevent axial separation in an axial direction. The compressor rotor disks are arranged in the axial direction with the tie rod extending through centers of the compressor disks. Adjacent compressor rotor disks are arranged such that opposing surfaces thereof are in tight contact with each other by being tightly fastened by the tie rod so that the adjacent compressor rotor disks cannot rotate relative to each other. Each of the compressor rotor disks has a plurality of compressor blades 1110 radially coupled to an outer circumferential surface thereof.

The compressor blades 1110 (or referred to as buckets) are radially coupled to an outer circumferential surface of each of the compressor rotor disks in a row. The compressor vanes 1120 (or referred to as nozzles) are mounted to an inner circumferential surface of the compressor housing in an annular row in each stage, and rows of the compressor vanes 1120 are arranged between rows of the compressor blades 1110. While the compressor disks rotate along with a rotation of the tie rod, the compressor vanes 1120 fixed to the housing do not rotate. The compressor vanes 1120 guide the flow of compressed air transferred from the compressor blades 1110 disposed at a preceding stage toward the compressor blades 1110 disposed at a following stage. In an exemplary embodiment, at least some of the plurality of compressor vanes 1120 may be mounted so as to be rotatable within a predetermined range, e.g., to adjust the flow rate of air.

The compressor 1100 may be operated using some of the power output from the turbine 1300. To this end, a rotating shaft of the compressor 1100 may be directly coupled with a rotating shaft of the turbine 1300 by the torque tube. In the case of a large gas turbine 1000, almost half of the output produced by the turbine 1300 may be consumed to drive the compressor 1100.

The tie rod is disposed to pass through centers of the plurality of compressor rotor disks and turbine rotor disks. One end of the tie rod is fastened to a compressor disk located at the foremost stage of the compressor 1100, and the other end thereof is fastened in the torque tube by a fastening nut.

It is understood that the tie rod is not limited to the example illustrated in FIG. 2, and may be changed or vary according to one or more other exemplary embodiments. For example, a single tie rod may be disposed to pass through the centers of the rotor disks, a plurality of tie rods may be arranged circumferentially, or a combination thereof may be used.

Also, a deswirler serving as a guide vane may be provided in the compressor 1100 to adjust an actual inflow angle of the fluid entering into an inlet of the combustor 1200 to a designed inflow angle.

The combustor 1200 mixes fuel with compressed air with fuel supplied from the compressor 1100, burns a fuel-air mixture to generate high-temperature and high-pressure combustion gas having high energy, and increases, through an isobaric combustion process, the temperature of the combustion gas to a temperature at which the combustor and the turbine components are able to withstand.

A plurality of combustors constituting the combustor 1200 of the gas turbine may be arranged in the housing in a form of a cell. The combustor 1200 may include a burner including a fuel injection nozzle, etc., a combustor liner forming a combustion chamber, and a transition piece serving as a connector between the combustor and the turbine.

The high-temperature and high-pressure combustion gas discharged from the combustor 1200 flows into the turbine 1300 and expands while passing through the inside of the turbine 1300, thereby applying an impulsive force or reaction force to the turbine blades 1310 to generate a rotational torque. A portion of the rotational torque is transmitted to the compressor 1110 via the torque tube, and a remaining portion which is an excessive torque is used to drive a generator to produce power.

The turbine 1300 basically has a structure similar to the compressor 1100. That is, the turbine 1300 may include a plurality of turbine rotors similar to the compressor rotors, and each of the turbine rotor may include a turbine rotor disk 1330 and a turbine blade 1310 fastened to the turbine rotor disk 1330. The turbine rotor disk 1330 has an approximately disk shape, and a plurality of slots are formed in an outer circumferential surface of the turbine rotor disk 1330. Each slot has a corrugated surface. The turbine blades 1310 are inserted into the respective slots. Each of the turbine blades 1310 may be coupled to the turbine rotor disk 1330 in a dovetail coupling manner. A plurality of turbine blades 1310 (or referred to as buckets) are radially disposed. A plurality of turbine vanes 1320 (or referred to as nozzles) are fixedly arranged on an inner circumferential surface of the turbine housing in an annular row in each stage, and rows of the turbine vanes 1320 are arranged between rows of the turbine blades 1310. The turbine vanes 1320 guide the flow direction of combustion gas passing through the turbine blades 1310.

FIG. 3 is a schematic diagram of the turbine 1300 illustrating a second stage bucket airfoil according to an exemplary embodiment. FIG. 4 is a perspective view of a turbine blade including an airfoil according to an exemplary embodiment. FIG. 5 is an alternative perspective view of the turbine blade including an airfoil of FIG. 4.

Referring to FIG. 3, the turbine 1300 may include a plurality of turbine stages employing a plurality of nozzles and a plurality of buckets. For example, a first stage comprises a plurality of circumferentially spaced nozzles 20 and turbine blades (or buckets) 10. The first stage nozzles 20 are circumferentially spaced one from the other and fixed about the axis of the rotor. The first stage buckets 10 may be mounted on a turbine rotor 17 for rotation about the rotor when high-temperature and high-pressure gases are expanded. A second stage of the turbine 1300 includes a plurality of circumferentially spaced nozzles 26 and blades (or buckets) 16 mounted on the turbine rotor 17. The second stage nozzles 26 are circumferentially spaced one from the other and fixed about the axis of the rotor. The second stage buckets 16 may be mounted on a turbine rotor 17 for rotation about the rotor when high-temperature and high-pressure gases are expanded. A third stage of the turbine 1300 includes a plurality of circumferentially spaced nozzles 32 and buckets 22 mounted on the turbine rotor 17. Although three stages are illustrated in FIG. 3, it is to be understood that any number of stages may be used.

Referring to FIGS. 4 and 5, the turbine blade 1310 according to the exemplary embodiment includes an airfoil 1340 having blade shape, a platform 1350 coupled to a lower portion of the airfoil 1340, a root member 1360 which protrudes downwards from the platform 1350 and is coupled to the rotor disk, and a tip shroud 1370 provided at a tip of the turbine blade 1310. Thus, the turbine blade 1310 has a blade airfoil profile at any cross-section from the platform 1350 to the tip shroud 1370 in the shape of the airfoil 1340. The turbine blade airfoil 1340 may be a curved plate having blade shape, and have an optimized blade shape according to specifications of the gas turbine 1000.

The turbine blade airfoil 1340 may include a leading edge LE disposed at an upstream side based on a flow direction of combustion gas, and a trailing edge TE disposed at a downstream side. Further, a suction side S1 protruding outward to have an outward-convex curved surface is formed on a front surface of the turbine blade airfoil 1340 onto which combustion gas is drawn, and a pressure side S2 having a curved surface depressed in a concaved shape toward the suction side S1 is formed on a rear surface of the turbine blade airfoil 1340. A difference in pressure occurs between the suction side S1 and the pressure side S2 of the turbine blade airfoil 1340, whereby the turbine 1300 is rotated.

The root member 1360 has a corrugated portion having an approximately dovetail shape corresponding to a dovetail-shaped corrugated portion formed in a slot of the rotor disk 1310. It is understood that the coupling structure of the root member 1360 is not limited thereto, and may be formed to have a fir-tree structure.

The platform 1350 may be disposed between the airfoil 1340 and the root member 1360 and have an approximately rectangular plate or rectangular pillar shape. The platform 1350 has a side surface which comes into contact with a side surface of the platform 1350 of an adjacent turbine blade 1310 to maintain an interval between the adjacent turbine blades 1310.

The airfoil shape may be defined by a loci of points in space that meet stage design requirements. These points are unique and specific to the system. The list of X, Y, and Z coordinates for the airfoil, which are included as Table 1, has been optimized for stage efficiency, aerodynamic efficiency, and thermal and mechanical life requirements. In one exemplary embodiment, the points may be arrived at by iteration between aerodynamic and mechanical design optimization. Accordingly, these are the only loci of points that allow the gas turbine to run at the most efficient, safe and smooth manner.

Referring to FIGS. 4 and 5, the airfoil shape of the exemplary embodiment is defined by a unique set or loci of points in space that may be delineated. As shown in Table 1, the loci that defines the shape of the airfoil may include a set of approximately 1,440 points with X, Y and Z coordinates. The X, Y and Z coordinates, which represent the airfoil shape, are created in a coordinate system which is defined relative to the cold rotor centerline axis of the gas turbine (i.e., X coordinate axis). The origin of the coordinate system on the cold rotor centerline axis is defined as X=0.0, Y=0.0 and Z=0.0. For example, the coordinate system is set relative to the airfoil and is fully defined by points A, B and C. Points A and B are both located 41.000 inches above the cold rotor centerline axis. Point A lies at an intersection of the airfoil mean camber line and the leading-edge airfoil surface. Point B lies at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface. Point C is located 48.440 inches above the cold rotor centerline axis and lies at the intersection of the airfoil mean camber line and the airfoil trailing-edge surface. Here, a coordinate system origin is located at point A. Points A and B define the positive X-axis. Points A, B and C define the positive X-Z plane. The Y-axis is then defined using the right-hand rule methodology. Thus, as illustrated, in some exemplary embodiments, the height of the airfoil may be approximately 9 to 11 inches. In some exemplary embodiments, the overall height of the bucket may be 16 to 18 inches. As described below, other heights are possible. The coordinate values for the X, Y and Z coordinates are set forth in inches in Table 1, although other units of dimensions may be used if the values are appropriately converted.

The Cartesian coordinate system of X, Y and Z values given in Table 1 below defines the shape of the airfoil according to an exemplary embodiment. More specifically, the shape of the airfoil is defined by the cloud of points listed such that airfoil could be constructed by defining approximately smooth sheet surfaces through the listed points. As one of ordinary skill in the art will appreciate, Table 1 values are generated and shown to three decimal places for determining the profile of airfoil. All of the 1,440 points represent a nominal cold or room temperature shape of the airfoil. It will be appreciated that as the bucket heats up in operation, mechanical loading and temperature will cause a change in X, Y and Z coordinates. Accordingly, values for the airfoil shape given in Table 1 represent ambient, non-operating or non-hot conditions.

The coordinate values set forth in Table 1 below are for a cold condition of the turbine blade (e.g., non-rotating state and at room temperature). Further, the coordinate values set forth in Table 1 are for an uncoated nominal three-dimensional (3D) shape of the turbine blade. In some aspects, a coating (e.g., corrosion protective coating) may be applied to the turbine bucket. The coating thickness may up to about 0.010 inches thick.

Further, the turbine blade 1310 may be fabricated using a variety of manufacturing techniques, such as forging, casting, milling, electro-chemical machining, electric-discharge machining, and the like. As such, the turbine blade may have a series of manufacturing tolerances for the position, profile, twist, and chord that can cause the turbine blade to vary from the nominal 3D shape defined by the coordinate values set forth in Table 1. This manufacturing tolerance may be, for example, +/−0.120 inches in a direction away from any of the coordinate values of Table 1 without departing from the scope of the subject matter described herein. In another aspects, the manufacturing tolerances may be +/−0.080 inches. In still another aspects, the manufacturing tolerances may be +/−0.020 inches.

In addition to manufacturing tolerances affecting the overall size of the turbine blade, it is also possible to scale the airfoil to a larger or smaller airfoil size. In order to maintain the benefits of this 3D shape, in terms of stiffness and stress, it is necessary to scale the turbine blade uniformly in the X, Y, and Z directions. Therefore, the coordinate values set forth in Table 1 may be scaled upwardly or downwardly such that the airfoil shape remains unchanged. The scaled version of the coordinates in Table 1 would be represented by X, Y and Z coordinate values of Table 1 with X and Y and Z coordinates multiplied or divided by a constant number.

The Table 1 values are generated and shown for determining the profile of the airfoil. There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/−values, including any coating thicknesses, are additive to the X, Y and Z values given in Table 1 below.

TABLE 1 X Y Z Section 1 Point 1 3.739 0.011 −0.930 Point 2 3.744 0.091 −0.931 Point 3 3.684 0.148 −0.932 Point 4 3.617 0.194 −0.932 Point 5 3.547 0.242 −0.933 Point 6 3.479 0.290 −0.933 Point 7 3.410 0.336 −0.934 Point 8 3.342 0.384 −0.935 Point 9 3.273 0.432 −0.935 Point 10 3.205 0.478 −0.936 Point 11 3.136 0.526 −0.936 Point 12 3.068 0.573 −0.937 Point 13 2.999 0.620 −0.937 Point 14 2.930 0.667 −0.938 Point 15 2.861 0.713 −0.938 Point 16 2.791 0.759 −0.939 Point 17 2.721 0.805 −0.940 Point 18 2.652 0.850 −0.940 Point 19 2.582 0.895 −0.941 Point 20 2.511 0.939 −0.941 Point 21 2.440 0.983 −0.942 Point 22 2.369 1.026 −0.942 Point 23 2.298 1.068 −0.943 Point 24 2.225 1.109 −0.943 Point 25 2.152 1.150 −0.944 Point 26 2.078 1.188 −0.944 Point 27 2.003 1.226 −0.944 Point 28 1.929 1.263 −0.945 Point 29 1.854 1.298 −0.945 Point 30 1.777 1.331 −0.946 Point 31 1.700 1.362 −0.946 Point 32 1.622 1.391 −0.946 Point 33 1.542 1.417 −0.947 Point 34 1.463 1.441 −0.947 Point 35 1.382 1.461 −0.947 Point 36 1.301 1.479 −0.947 Point 37 1.218 1.491 −0.948 Point 38 1.135 1.499 −0.948 Point 39 1.052 1.503 −0.948 Point 40 0.968 1.500 −0.948 Point 41 0.886 1.492 −0.948 Point 42 0.804 1.477 −0.947 Point 43 0.723 1.455 −0.947 Point 44 0.645 1.427 −0.947 Point 45 0.570 1.392 −0.946 Point 46 0.497 1.352 −0.946 Point 47 0.428 1.305 −0.945 Point 48 0.363 1.253 −0.945 Point 49 0.302 1.196 −0.944 Point 50 0.244 1.136 −0.943 Point 51 0.191 1.072 −0.943 Point 52 0.143 1.004 −0.942 Point 53 0.097 0.935 −0.941 Point 54 0.055 0.863 −0.940 Point 55 0.018 0.788 −0.939 Point 56 −0.018 0.712 −0.938 Point 57 −0.049 0.635 −0.938 Point 58 −0.077 0.557 −0.937 Point 59 −0.102 0.478 −0.936 Point 60 −0.124 0.397 −0.935 Point 61 −0.142 0.316 −0.934 Point 62 −0.155 0.234 −0.933 Point 63 −0.165 0.152 −0.932 Point 64 −0.168 0.068 −0.931 Point 65 −0.163 −0.015 −0.930 Point 66 −0.143 −0.096 −0.929 Point 67 −0.098 −0.164 −0.928 Point 68 −0.022 −0.193 −0.928 Point 69 0.053 −0.160 −0.928 Point 70 0.112 −0.101 −0.929 Point 71 0.163 −0.035 −0.930 Point 72 0.213 0.032 −0.930 Point 73 0.260 0.101 −0.931 Point 74 0.308 0.169 −0.932 Point 75 0.357 0.236 −0.933 Point 76 0.407 0.302 −0.934 Point 77 0.459 0.368 −0.934 Point 78 0.512 0.431 −0.935 Point 79 0.569 0.493 −0.936 Point 80 0.628 0.551 −0.937 Point 81 0.689 0.607 −0.937 Point 82 0.754 0.660 −0.938 Point 83 0.822 0.708 −0.938 Point 84 0.894 0.751 −0.939 Point 85 0.967 0.789 −0.939 Point 86 1.044 0.820 −0.940 Point 87 1.124 0.846 −0.940 Point 88 1.205 0.864 −0.940 Point 89 1.287 0.877 −0.940 Point 90 1.370 0.882 −0.940 Point 91 1.454 0.882 −0.940 Point 92 1.537 0.877 −0.940 Point 93 1.620 0.867 −0.940 Point 94 1.701 0.852 −0.940 Point 95 1.783 0.834 −0.940 Point 96 1.863 0.813 −0.940 Point 97 1.943 0.789 −0.939 Point 98 2.022 0.763 −0.939 Point 99 2.100 0.734 −0.939 Point 100 2.178 0.704 −0.938 Point 101 2.255 0.672 −0.938 Point 102 2.332 0.639 −0.938 Point 103 2.408 0.606 −0.937 Point 104 2.484 0.570 −0.937 Point 105 2.559 0.534 −0.936 Point 106 2.634 0.498 −0.936 Point 107 2.708 0.461 −0.935 Point 108 2.782 0.424 −0.935 Point 109 2.856 0.385 −0.935 Point 110 2.931 0.348 −0.934 Point 111 3.004 0.309 −0.934 Point 112 3.078 0.270 −0.933 Point 113 3.152 0.231 −0.933 Point 114 3.225 0.191 −0.932 Point 115 3.299 0.153 −0.932 Point 116 3.372 0.113 −0.931 Point 117 3.445 0.074 −0.931 Point 118 3.519 0.035 −0.930 Point 119 3.593 −0.005 −0.930 Point 120 3.670 −0.031 −0.930 Section 2 Point 1 3.716 0.000 0.000 Point 2 3.722 0.078 −0.001 Point 3 3.6659 0.133 −0.002 Point 4 3.599 0.181 −0.002 Point 5 3.535 0.228 −0.003 Point 6 3.469 0.276 −0.003 Point 7 3.403 0.324 −0.004 Point 8 3.338 0.371 −0.004 Point 9 3.273 0.419 −0.005 Point 10 3.207 0.466 −0.005 Point 11 3.142 0.513 −0.006 Point 12 3.076 0.561 −0.007 Point 13 3.010 0.608 −0.007 Point 14 2.943 0.654 −0.008 Point 15 2.877 0.700 −0.008 Point 16 2.811 0.746 −0.009 Point 17 2.743 0.792 −0.009 Point 18 2.677 0.838 −0.010 Point 19 2.609 0.882 −0.010 Point 20 2.542 0.926 −0.011 Point 21 2.474 0.970 −0.011 Point 22 2.406 1.013 −0.012 Point 23 2.337 1.056 −0.012 Point 24 2.267 1.097 −0.013 Point 25 2.198 1.138 −0.013 Point 26 2.128 1.178 −0.014 Point 27 2.056 1.216 −0.014 Point 28 1.985 1.254 −0.015 Point 29 1.912 1.290 −0.015 Point 30 1.840 1.325 −0.016 Point 31 1.765 1.358 −0.016 Point 32 1.691 1.390 −0.016 Point 33 1.615 1.419 −0.017 Point 34 1.539 1.445 −0.017 Point 35 1.462 1.469 −0.017 Point 36 1.384 1.491 −0.018 Point 37 1.305 1.508 −0.018 Point 38 1.225 1.522 −0.018 Point 39 1.145 1.533 −0.018 Point 40 1.064 1.537 −0.018 Point 41 0.984 1.537 −0.018 Point 42 0.902 1.532 −0.018 Point 43 0.823 1.520 −0.018 Point 44 0.743 1.502 −0.018 Point 45 0.667 1.477 −0.017 Point 46 0.592 1.446 −0.017 Point 47 0.521 1.409 −0.017 Point 48 0.451 1.366 −0.016 Point 49 0.387 1.318 −0.016 Point 50 0.326 1.265 −0.015 Point 51 0.269 1.208 −0.014 Point 52 0.216 1.147 −0.013 Point 53 0.167 1.082 −0.013 Point 54 0.121 1.015 −0.012 Point 55 0.079 0.946 −0.011 Point 56 0.041 0.875 −0.010 Point 57 0.007 0.802 −0.009 Point 58 −0.024 0.727 −0.009 Point 59 −0.051 0.651 −0.008 Point 60 −0.075 0.573 −0.007 Point 61 −0.094 0.495 −0.006 Point 62 −0.110 0.416 −0.005 Point 63 −0.120 0.335 −0.004 Point 64 −0.123 0.254 −0.003 Point 65 −0.118 0.174 −0.002 Point 66 −0.099 0.096 −0.001 Point 67 −0.055 0.028 0.000 Point 68 0.019 −0.002 0.000 Point 69 0.093 0.026 0.000 Point 70 0.154 0.079 −0.001 Point 71 0.207 0.140 −0.002 Point 72 0.257 0.203 −0.002 Point 73 0.306 0.268 −0.003 Point 74 0.355 0.332 −0.004 Point 75 0.405 0.396 −0.005 Point 76 0.455 0.459 −0.005 Point 77 0.509 0.520 −0.006 Point 78 0.564 0.578 −0.007 Point 79 0.622 0.635 −0.007 Point 80 0.683 0.688 −0.008 Point 81 0.747 0.737 −0.009 Point 82 0.815 0.782 −0.009 Point 83 0.886 0.821 −0.010 Point 84 0.959 0.854 −0.010 Point 85 1.036 0.881 −0.010 Point 86 1.115 0.901 −0.011 Point 87 1.194 0.915 −0.011 Point 88 1.275 0.922 −0.011 Point 89 1.355 0.924 −0.011 Point 90 1.436 0.919 −0.011 Point 91 1.516 0.911 −0.011 Point 92 1.596 0.898 −0.011 Point 93 1.676 0.881 −0.010 Point 94 1.754 0.862 −0.010 Point 95 1.831 0.839 −0.010 Point 96 1.909 0.814 −0.010 Point 97 1.985 0.787 −0.009 Point 98 2.061 0.759 −0.009 Point 99 2.135 0.729 −0.009 Point 100 2.210 0.697 −0.008 Point 101 2.284 0.664 −0.008 Point 102 2.357 0.631 −0.007 Point 103 2.431 0.596 −0.007 Point 104 2.504 0.562 −0.007 Point 105 2.576 0.526 −0.006 Point 106 2.648 0.489 −0.006 Point 107 2.720 0.452 −0.005 Point 108 2.793 0.415 −0.005 Point 109 2.864 0.377 −0.004 Point 110 2.935 0.340 −0.004 Point 111 3.007 0.301 −0.004 Point 112 3.077 0.263 −0.003 Point 113 3.149 0.225 −0.003 Point 114 3.220 0.186 −0.002 Point 115 3.290 0.147 −0.002 Point 116 3.361 0.108 −0.001 Point 117 3.432 0.068 −0.001 Point 118 3.503 0.029 0.000 Point 119 3.574 −0.010 0.000 Point 120 3.649 −0.039 0.000 Section 3 Point 1 3.669 −0.012 0.930 Point 2 3.676 0.063 0.929 Point 3 3.622 0.117 0.929 Point 4 3.560 0.165 0.928 Point 5 3.498 0.213 0.928 Point 6 3.436 0.260 0.927 Point 7 3.374 0.307 0.926 Point 8 3.312 0.355 0.926 Point 9 3.250 0.401 0.925 Point 10 3.187 0.448 0.925 Point 11 3.125 0.495 0.924 Point 12 3.063 0.542 0.924 Point 13 3.001 0.588 0.923 Point 14 2.938 0.635 0.923 Point 15 2.875 0.681 0.922 Point 16 2.812 0.726 0.922 Point 17 2.748 0.771 0.921 Point 18 2.684 0.816 0.920 Point 19 2.620 0.861 0.920 Point 20 2.556 0.905 0.919 Point 21 2.492 0.948 0.919 Point 22 2.426 0.992 0.918 Point 23 2.361 1.034 0.918 Point 24 2.295 1.076 0.917 Point 25 2.228 1.116 0.917 Point 26 2.161 1.156 0.916 Point 27 2.094 1.195 0.916 Point 28 2.026 1.233 0.916 Point 29 1.957 1.270 0.915 Point 30 1.888 1.305 0.915 Point 31 1.818 1.339 0.914 Point 32 1.747 1.372 0.914 Point 33 1.675 1.402 0.914 Point 34 1.603 1.430 0.913 Point 35 1.529 1.456 0.913 Point 36 1.454 1.480 0.913 Point 37 1.379 1.499 0.912 Point 38 1.303 1.517 0.912 Point 39 1.226 1.530 0.912 Point 40 1.149 1.540 0.912 Point 41 1.072 1.544 0.912 Point 42 0.993 1.544 0.912 Point 43 0.916 1.538 0.912 Point 44 0.838 1.527 0.912 Point 45 0.763 1.509 0.912 Point 46 0.688 1.486 0.913 Point 47 0.616 1.457 0.913 Point 48 0.546 1.423 0.913 Point 49 0.480 1.383 0.914 Point 50 0.416 1.338 0.914 Point 51 0.356 1.288 0.915 Point 52 0.299 1.234 0.916 Point 53 0.246 1.177 0.916 Point 54 0.197 1.117 0.917 Point 55 0.151 1.053 0.918 Point 56 0.110 0.988 0.918 Point 57 0.072 0.920 0.919 Point 58 0.037 0.850 0.920 Point 59 0.007 0.779 0.921 Point 60 −0.020 0.705 0.922 Point 61 −0.042 0.631 0.923 Point 62 −0.059 0.554 0.924 Point 63 −0.071 0.477 0.924 Point 64 −0.075 0.400 0.925 Point 65 −0.069 0.322 0.926 Point 66 −0.048 0.247 0.927 Point 67 0.000 0.186 0.928 Point 68 0.073 0.165 0.928 Point 69 0.144 0.194 0.928 Point 70 0.203 0.246 0.927 Point 71 0.255 0.304 0.926 Point 72 0.305 0.363 0.926 Point 73 0.354 0.424 0.925 Point 74 0.403 0.484 0.924 Point 75 0.454 0.543 0.924 Point 76 0.507 0.601 0.923 Point 77 0.562 0.656 0.922 Point 78 0.619 0.709 0.922 Point 79 0.680 0.758 0.921 Point 80 0.743 0.803 0.921 Point 81 0.811 0.843 0.920 Point 82 0.881 0.877 0.920 Point 83 0.953 0.905 0.919 Point 84 1.027 0.927 0.919 Point 85 1.104 0.942 0.919 Point 86 1.181 0.951 0.919 Point 87 1.260 0.955 0.919 Point 88 1.337 0.953 0.919 Point 89 1.415 0.946 0.919 Point 90 1.493 0.935 0.919 Point 91 1.569 0.920 0.919 Point 92 1.645 0.902 0.919 Point 93 1.720 0.881 0.920 Point 94 1.794 0.858 0.920 Point 95 1.868 0.833 0.920 Point 96 1.942 0.806 0.921 Point 97 2.014 0.778 0.921 Point 98 2.085 0.748 0.921 Point 99 2.157 0.717 0.922 Point 100 2.228 0.684 0.922 Point 101 2.299 0.651 0.922 Point 102 2.369 0.617 0.923 Point 103 2.439 0.582 0.923 Point 104 2.509 0.547 0.924 Point 105 2.578 0.512 0.924 Point 106 2.646 0.475 0.924 Point 107 2.716 0.439 0.925 Point 108 2.785 0.403 0.925 Point 109 2.852 0.365 0.926 Point 110 2.921 0.328 0.926 Point 111 2.989 0.290 0.927 Point 112 3.058 0.252 0.927 Point 113 3.126 0.214 0.928 Point 114 3.193 0.175 0.928 Point 115 3.261 0.137 0.928 Point 116 3.329 0.098 0.929 Point 117 3.396 0.060 0.929 Point 118 3.464 0.021 0.930 Point 119 3.532 −0.018 0.930 Point 120 3.603 −0.046 0.931 Section 4 Point 1 3.585 −0.024 1.860 Point 2 3.593 0.048 1.860 Point 3 3.541 0.101 1.859 Point 4 3.483 0.148 1.858 Point 5 3.423 0.194 1.858 Point 6 3.364 0.241 1.857 Point 7 3.305 0.288 1.857 Point 8 3.246 0.334 1.856 Point 9 3.186 0.380 1.856 Point 10 3.126 0.427 1.855 Point 11 3.067 0.473 1.855 Point 12 3.007 0.519 1.854 Point 13 2.947 0.564 1.853 Point 14 2.888 0.611 1.853 Point 15 2.827 0.655 1.852 Point 16 2.767 0.700 1.852 Point 17 2.707 0.745 1.851 Point 18 2.646 0.790 1.851 Point 19 2.585 0.833 1.850 Point 20 2.524 0.878 1.850 Point 21 2.462 0.921 1.849 Point 22 2.399 0.964 1.849 Point 23 2.337 1.006 1.848 Point 24 2.275 1.047 1.848 Point 25 2.212 1.089 1.847 Point 26 2.148 1.129 1.847 Point 27 2.084 1.169 1.846 Point 28 2.020 1.207 1.846 Point 29 1.955 1.246 1.845 Point 30 1.888 1.282 1.845 Point 31 1.822 1.318 1.845 Point 32 1.755 1.352 1.844 Point 33 1.688 1.385 1.844 Point 34 1.619 1.417 1.843 Point 35 1.550 1.446 1.843 Point 36 1.480 1.474 1.843 Point 37 1.409 1.499 1.843 Point 38 1.337 1.522 1.842 Point 39 1.264 1.542 1.842 Point 40 1.191 1.559 1.842 Point 41 1.116 1.572 1.842 Point 42 1.042 1.582 1.842 Point 43 0.967 1.587 1.841 Point 44 0.891 1.587 1.841 Point 45 0.816 1.583 1.842 Point 46 0.742 1.573 1.842 Point 47 0.668 1.557 1.842 Point 48 0.596 1.535 1.842 Point 49 0.526 1.508 1.842 Point 50 0.458 1.476 1.843 Point 51 0.393 1.437 1.843 Point 52 0.332 1.394 1.844 Point 53 0.274 1.345 1.844 Point 54 0.220 1.293 1.845 Point 55 0.170 1.237 1.846 Point 56 0.125 1.177 1.846 Point 57 0.083 1.114 1.847 Point 58 0.045 1.048 1.848 Point 59 0.012 0.981 1.849 Point 60 −0.016 0.912 1.849 Point 61 −0.041 0.840 1.850 Point 62 −0.059 0.767 1.851 Point 63 −0.070 0.692 1.852 Point 64 −0.075 0.618 1.853 Point 65 −0.067 0.543 1.854 Point 66 −0.041 0.473 1.855 Point 67 0.011 0.419 1.855 Point 68 0.084 0.409 1.855 Point 69 0.150 0.446 1.855 Point 70 0.204 0.498 1.854 Point 71 0.254 0.554 1.854 Point 72 0.302 0.612 1.853 Point 73 0.352 0.669 1.852 Point 74 0.402 0.725 1.852 Point 75 0.456 0.777 1.851 Point 76 0.512 0.827 1.850 Point 77 0.572 0.873 1.850 Point 78 0.636 0.914 1.849 Point 79 0.702 0.949 1.849 Point 80 0.771 0.978 1.849 Point 81 0.843 1.001 1.848 Point 82 0.916 1.017 1.848 Point 83 0.991 1.027 1.848 Point 84 1.066 1.031 1.848 Point 85 1.141 1.030 1.848 Point 86 1.217 1.024 1.848 Point 87 1.292 1.014 1.848 Point 88 1.365 1.000 1.848 Point 89 1.439 0.983 1.849 Point 90 1.511 0.963 1.849 Point 91 1.584 0.942 1.849 Point 92 1.655 0.917 1.849 Point 93 1.725 0.891 1.850 Point 94 1.796 0.863 1.850 Point 95 1.865 0.835 1.850 Point 96 1.934 0.805 1.851 Point 97 2.002 0.773 1.851 Point 98 2.071 0.741 1.851 Point 99 2.138 0.708 1.852 Point 100 2.206 0.675 1.852 Point 101 2.273 0.640 1.853 Point 102 2.340 0.606 1.853 Point 103 2.406 0.571 1.853 Point 104 2.473 0.535 1.854 Point 105 2.539 0.499 1.854 Point 106 2.605 0.463 1.855 Point 107 2.671 0.426 1.855 Point 108 2.736 0.389 1.856 Point 109 2.802 0.352 1.856 Point 110 2.867 0.315 1.856 Point 111 2.932 0.277 1.857 Point 112 2.998 0.240 1.857 Point 113 3.063 0.201 1.858 Point 114 3.128 0.163 1.858 Point 115 3.193 0.126 1.859 Point 116 3.258 0.088 1.859 Point 117 3.322 0.049 1.860 Point 118 3.387 0.011 1.860 Point 119 3.452 −0.028 1.860 Point 120 3.521 −0.057 1.861 Section 5 Point 1 3.501 −0.029 2.791 Point 2 3.509 0.041 2.790 Point 3 3.459 0.094 2.789 Point 4 3.402 0.140 2.789 Point 5 3.344 0.187 2.788 Point 6 3.288 0.233 2.787 Point 7 3.230 0.279 2.787 Point 8 3.173 0.326 2.786 Point 9 3.116 0.371 2.786 Point 10 3.059 0.417 2.785 Point 11 3.001 0.463 2.785 Point 12 2.944 0.510 2.784 Point 13 2.885 0.554 2.784 Point 14 2.827 0.599 2.783 Point 15 2.770 0.645 2.783 Point 16 2.711 0.690 2.782 Point 17 2.653 0.735 2.782 Point 18 2.594 0.779 2.781 Point 19 2.535 0.823 2.781 Point 20 2.476 0.867 2.780 Point 21 2.417 0.910 2.779 Point 22 2.357 0.953 2.779 Point 23 2.297 0.996 2.778 Point 24 2.237 1.039 2.778 Point 25 2.176 1.080 2.777 Point 26 2.115 1.121 2.777 Point 27 2.054 1.161 2.777 Point 28 1.992 1.201 2.776 Point 29 1.929 1.240 2.776 Point 30 1.866 1.279 2.775 Point 31 1.803 1.316 2.775 Point 32 1.739 1.352 2.774 Point 33 1.675 1.388 2.774 Point 34 1.609 1.421 2.773 Point 35 1.544 1.454 2.773 Point 36 1.477 1.486 2.773 Point 37 1.410 1.515 2.772 Point 38 1.342 1.543 2.772 Point 39 1.273 1.568 2.772 Point 40 1.203 1.592 2.771 Point 41 1.132 1.612 2.771 Point 42 1.061 1.629 2.771 Point 43 0.989 1.643 2.771 Point 44 0.916 1.653 2.771 Point 45 0.842 1.659 2.771 Point 46 0.768 1.660 2.771 Point 47 0.695 1.657 2.771 Point 48 0.623 1.646 2.771 Point 49 0.551 1.631 2.771 Point 50 0.480 1.608 2.771 Point 51 0.412 1.580 2.772 Point 52 0.347 1.546 2.772 Point 53 0.286 1.506 2.772 Point 54 0.227 1.460 2.773 Point 55 0.174 1.410 2.774 Point 56 0.125 1.356 2.774 Point 57 0.080 1.297 2.775 Point 58 0.039 1.236 2.776 Point 59 0.004 1.171 2.776 Point 60 −0.027 1.104 2.777 Point 61 −0.053 1.035 2.778 Point 62 −0.072 0.965 2.779 Point 63 −0.084 0.892 2.780 Point 64 −0.087 0.819 2.781 Point 65 −0.077 0.746 2.781 Point 66 −0.045 0.680 2.782 Point 67 0.012 0.637 2.783 Point 68 0.084 0.640 2.783 Point 69 0.144 0.682 2.782 Point 70 0.195 0.735 2.782 Point 71 0.244 0.791 2.781 Point 72 0.292 0.846 2.780 Point 73 0.343 0.899 2.780 Point 74 0.397 0.949 2.779 Point 75 0.453 0.995 2.778 Point 76 0.515 1.036 2.778 Point 77 0.579 1.071 2.778 Point 78 0.648 1.099 2.777 Point 79 0.718 1.120 2.777 Point 80 0.790 1.134 2.777 Point 81 0.864 1.140 2.777 Point 82 0.937 1.140 2.777 Point 83 1.011 1.136 2.777 Point 84 1.084 1.125 2.777 Point 85 1.156 1.112 2.777 Point 86 1.228 1.095 2.777 Point 87 1.299 1.075 2.778 Point 88 1.368 1.053 2.778 Point 89 1.438 1.029 2.778 Point 90 1.507 1.002 2.778 Point 91 1.575 0.975 2.779 Point 92 1.642 0.945 2.779 Point 93 1.709 0.915 2.779 Point 94 1.776 0.884 2.780 Point 95 1.842 0.851 2.780 Point 96 1.908 0.819 2.781 Point 97 1.973 0.785 2.781 Point 98 2.039 0.751 2.781 Point 99 2.104 0.717 2.782 Point 100 2.169 0.681 2.782 Point 101 2.232 0.646 2.783 Point 102 2.297 0.611 2.783 Point 103 2.361 0.574 2.783 Point 104 2.424 0.537 2.784 Point 105 2.489 0.501 2.784 Point 106 2.552 0.464 2.785 Point 107 2.615 0.427 2.785 Point 108 2.679 0.389 2.786 Point 109 2.742 0.352 2.786 Point 110 2.806 0.314 2.786 Point 111 2.868 0.276 2.787 Point 112 2.931 0.238 2.787 Point 113 2.995 0.200 2.788 Point 114 3.058 0.161 2.788 Point 115 3.120 0.123 2.789 Point 116 3.183 0.085 2.789 Point 117 3.246 0.047 2.790 Point 118 3.309 0.008 2.790 Point 119 3.371 −0.030 2.791 Point 120 3.437 −0.060 2.791 Section 6 Point 1 3.431 −0.027 3.721 Point 2 3.440 0.042 3.720 Point 3 3.392 0.095 3.719 Point 4 3.336 0.141 3.719 Point 5 3.281 0.188 3.718 Point 6 3.226 0.234 3.717 Point 7 3.170 0.281 3.717 Point 8 3.115 0.328 3.716 Point 9 3.060 0.374 3.716 Point 10 3.004 0.420 3.715 Point 11 2.948 0.465 3.715 Point 12 2.893 0.511 3.714 Point 13 2.836 0.557 3.714 Point 14 2.780 0.603 3.713 Point 15 2.724 0.648 3.713 Point 16 2.667 0.694 3.712 Point 17 2.611 0.738 3.712 Point 18 2.554 0.783 3.711 Point 19 2.496 0.828 3.711 Point 20 2.439 0.872 3.710 Point 21 2.382 0.916 3.709 Point 22 2.325 0.959 3.709 Point 23 2.266 1.002 3.708 Point 24 2.208 1.045 3.708 Point 25 2.149 1.087 3.707 Point 26 2.090 1.128 3.707 Point 27 2.031 1.171 3.706 Point 28 1.971 1.211 3.706 Point 29 1.911 1.251 3.706 Point 30 1.851 1.290 3.705 Point 31 1.789 1.329 3.705 Point 32 1.727 1.367 3.704 Point 33 1.665 1.403 3.704 Point 34 1.603 1.439 3.703 Point 35 1.539 1.474 3.703 Point 36 1.476 1.507 3.703 Point 37 1.410 1.540 3.702 Point 38 1.344 1.570 3.702 Point 39 1.278 1.598 3.701 Point 40 1.211 1.625 3.701 Point 41 1.144 1.649 3.701 Point 42 1.074 1.671 3.701 Point 43 1.005 1.691 3.700 Point 44 0.934 1.706 3.700 Point 45 0.862 1.718 3.700 Point 46 0.790 1.726 3.700 Point 47 0.719 1.728 3.700 Point 48 0.646 1.725 3.700 Point 49 0.574 1.717 3.700 Point 50 0.503 1.704 3.700 Point 51 0.435 1.683 3.700 Point 52 0.367 1.655 3.701 Point 53 0.303 1.622 3.701 Point 54 0.243 1.583 3.702 Point 55 0.186 1.538 3.702 Point 56 0.134 1.488 3.703 Point 57 0.086 1.434 3.703 Point 58 0.042 1.376 3.704 Point 59 0.004 1.314 3.705 Point 60 −0.029 1.251 3.706 Point 61 −0.056 1.183 3.706 Point 62 −0.076 1.114 3.707 Point 63 −0.090 1.043 3.708 Point 64 −0.093 0.971 3.709 Point 65 −0.080 0.900 3.710 Point 66 −0.045 0.838 3.710 Point 67 0.017 0.803 3.711 Point 68 0.087 0.816 3.711 Point 69 0.144 0.861 3.710 Point 70 0.194 0.912 3.710 Point 71 0.243 0.965 3.709 Point 72 0.294 1.017 3.708 Point 73 0.347 1.066 3.708 Point 74 0.404 1.111 3.707 Point 75 0.464 1.150 3.707 Point 76 0.528 1.183 3.706 Point 77 0.596 1.208 3.706 Point 78 0.666 1.226 3.706 Point 79 0.738 1.236 3.706 Point 80 0.810 1.238 3.706 Point 81 0.883 1.235 3.706 Point 82 0.954 1.226 3.706 Point 83 1.025 1.213 3.706 Point 84 1.095 1.196 3.706 Point 85 1.165 1.176 3.706 Point 86 1.234 1.153 3.707 Point 87 1.301 1.128 3.707 Point 88 1.368 1.101 3.707 Point 89 1.435 1.072 3.708 Point 90 1.500 1.042 3.708 Point 91 1.566 1.012 3.708 Point 92 1.630 0.980 3.709 Point 93 1.695 0.947 3.709 Point 94 1.759 0.913 3.710 Point 95 1.823 0.879 3.710 Point 96 1.886 0.844 3.710 Point 97 1.950 0.810 3.711 Point 98 2.012 0.773 3.711 Point 99 2.075 0.737 3.712 Point 100 2.137 0.701 3.712 Point 101 2.200 0.664 3.712 Point 102 2.261 0.627 3.713 Point 103 2.324 0.590 3.713 Point 104 2.385 0.552 3.714 Point 105 2.448 0.515 3.714 Point 106 2.509 0.477 3.715 Point 107 2.570 0.439 3.715 Point 108 2.632 0.401 3.716 Point 109 2.693 0.362 3.716 Point 110 2.754 0.324 3.716 Point 111 2.816 0.286 3.717 Point 112 2.877 0.248 3.717 Point 113 2.937 0.208 3.718 Point 114 2.999 0.170 3.718 Point 115 3.060 0.132 3.719 Point 116 3.121 0.092 3.719 Point 117 3.182 0.053 3.720 Point 118 3.243 0.014 3.720 Point 119 3.304 −0.024 3.721 Point 120 3.368 −0.056 3.721 Section 7 Point 1 3.369 −0.020 4.651 Point 2 3.379 0.047 4.650 Point 3 3.332 0.099 4.649 Point 4 3.278 0.146 4.649 Point 5 3.225 0.192 4.648 Point 6 3.172 0.239 4.648 Point 7 3.118 0.286 4.647 Point 8 3.065 0.333 4.646 Point 9 3.010 0.379 4.646 Point 10 2.956 0.425 4.645 Point 11 2.903 0.472 4.645 Point 12 2.849 0.518 4.644 Point 13 2.794 0.564 4.644 Point 14 2.739 0.609 4.643 Point 15 2.685 0.655 4.643 Point 16 2.630 0.700 4.642 Point 17 2.575 0.745 4.642 Point 18 2.521 0.790 4.641 Point 19 2.465 0.835 4.640 Point 20 2.410 0.879 4.640 Point 21 2.353 0.924 4.639 Point 22 2.298 0.968 4.639 Point 23 2.242 1.011 4.638 Point 24 2.185 1.054 4.638 Point 25 2.128 1.097 4.637 Point 26 2.071 1.140 4.637 Point 27 2.015 1.182 4.636 Point 28 1.956 1.223 4.636 Point 29 1.899 1.264 4.635 Point 30 1.840 1.304 4.635 Point 31 1.780 1.344 4.635 Point 32 1.721 1.382 4.634 Point 33 1.660 1.420 4.634 Point 34 1.600 1.458 4.633 Point 35 1.539 1.493 4.633 Point 36 1.477 1.529 4.632 Point 37 1.414 1.563 4.632 Point 38 1.351 1.594 4.632 Point 39 1.287 1.625 4.631 Point 40 1.222 1.655 4.631 Point 41 1.156 1.681 4.631 Point 42 1.090 1.706 4.630 Point 43 1.022 1.729 4.630 Point 44 0.954 1.748 4.630 Point 45 0.885 1.764 4.630 Point 46 0.815 1.777 4.629 Point 47 0.744 1.785 4.629 Point 48 0.673 1.788 4.629 Point 49 0.601 1.786 4.629 Point 50 0.531 1.778 4.629 Point 51 0.462 1.764 4.630 Point 52 0.393 1.743 4.630 Point 53 0.327 1.717 4.630 Point 54 0.265 1.684 4.631 Point 55 0.205 1.645 4.631 Point 56 0.150 1.600 4.631 Point 57 0.100 1.551 4.632 Point 58 0.053 1.496 4.633 Point 59 0.013 1.438 4.633 Point 60 −0.023 1.377 4.634 Point 61 −0.052 1.312 4.635 Point 62 −0.075 1.245 4.636 Point 63 −0.090 1.175 4.636 Point 64 −0.092 1.105 4.637 Point 65 −0.078 1.035 4.638 Point 66 −0.038 0.977 4.639 Point 67 0.026 0.949 4.639 Point 68 0.093 0.968 4.639 Point 69 0.150 1.011 4.638 Point 70 0.202 1.059 4.638 Point 71 0.252 1.109 4.637 Point 72 0.305 1.157 4.637 Point 73 0.361 1.200 4.636 Point 74 0.422 1.239 4.636 Point 75 0.485 1.271 4.635 Point 76 0.552 1.296 4.635 Point 77 0.620 1.313 4.635 Point 78 0.691 1.321 4.635 Point 79 0.762 1.323 4.635 Point 80 0.832 1.318 4.635 Point 81 0.903 1.307 4.635 Point 82 0.973 1.292 4.635 Point 83 1.041 1.273 4.635 Point 84 1.109 1.251 4.636 Point 85 1.176 1.227 4.636 Point 86 1.242 1.200 4.636 Point 87 1.307 1.172 4.637 Point 88 1.372 1.143 4.637 Point 89 1.436 1.112 4.637 Point 90 1.499 1.080 4.638 Point 91 1.561 1.047 4.638 Point 92 1.624 1.013 4.638 Point 93 1.687 0.978 4.639 Point 94 1.748 0.942 4.639 Point 95 1.810 0.907 4.640 Point 96 1.870 0.871 4.640 Point 97 1.931 0.834 4.641 Point 98 1.992 0.797 4.641 Point 99 2.053 0.760 4.641 Point 100 2.113 0.723 4.642 Point 101 2.174 0.685 4.642 Point 102 2.234 0.646 4.643 Point 103 2.294 0.609 4.643 Point 104 2.353 0.570 4.644 Point 105 2.413 0.532 4.644 Point 106 2.472 0.493 4.645 Point 107 2.532 0.454 4.645 Point 108 2.592 0.415 4.645 Point 109 2.652 0.376 4.646 Point 110 2.710 0.337 4.646 Point 111 2.770 0.298 4.647 Point 112 2.829 0.259 4.647 Point 113 2.889 0.220 4.648 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1.314 5.565 Point 31 1.771 1.353 5.564 Point 32 1.714 1.393 5.564 Point 33 1.655 1.432 5.564 Point 34 1.597 1.471 5.563 Point 35 1.538 1.508 5.563 Point 36 1.478 1.545 5.562 Point 37 1.418 1.580 5.562 Point 38 1.357 1.614 5.561 Point 39 1.296 1.647 5.561 Point 40 1.233 1.678 5.561 Point 41 1.170 1.708 5.560 Point 42 1.106 1.736 5.560 Point 43 1.041 1.761 5.560 Point 44 0.975 1.785 5.559 Point 45 0.908 1.805 5.559 Point 46 0.841 1.822 5.559 Point 47 0.772 1.836 5.559 Point 48 0.702 1.846 5.559 Point 49 0.633 1.851 5.559 Point 50 0.563 1.850 5.559 Point 51 0.494 1.843 5.559 Point 52 0.425 1.831 5.559 Point 53 0.358 1.812 5.559 Point 54 0.293 1.786 5.559 Point 55 0.231 1.753 5.560 Point 56 0.173 1.714 5.560 Point 57 0.119 1.670 5.561 Point 58 0.070 1.620 5.561 Point 59 0.027 1.566 5.562 Point 60 −0.012 1.507 5.563 Point 61 −0.044 1.445 5.563 Point 62 −0.068 1.380 5.564 Point 63 −0.085 1.312 5.565 Point 64 −0.088 1.242 5.566 Point 65 −0.070 1.175 5.567 Point 66 −0.027 1.122 5.567 Point 67 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104 2.322 0.584 5.574 Point 105 2.380 0.545 5.574 Point 106 2.438 0.506 5.574 Point 107 2.495 0.466 5.575 Point 108 2.552 0.426 5.575 Point 109 2.610 0.387 5.576 Point 110 2.668 0.347 5.576 Point 111 2.725 0.307 5.577 Point 112 2.783 0.268 5.577 Point 113 2.841 0.228 5.578 Point 114 2.898 0.188 5.578 Point 115 2.955 0.148 5.579 Point 116 3.013 0.109 5.579 Point 117 3.070 0.069 5.580 Point 118 3.128 0.030 5.580 Point 119 3.186 −0.010 5.581 Point 120 3.247 −0.042 5.581 Section 9 Point 1 3.246 −0.011 6.511 Point 2 3.258 0.054 6.510 Point 3 3.215 0.107 6.509 Point 4 3.165 0.153 6.509 Point 5 3.115 0.201 6.508 Point 6 3.064 0.247 6.508 Point 7 3.013 0.294 6.507 Point 8 2.962 0.341 6.506 Point 9 2.912 0.387 6.506 Point 10 2.861 0.433 6.505 Point 11 2.810 0.480 6.505 Point 12 2.759 0.526 6.504 Point 13 2.708 0.572 6.504 Point 14 2.657 0.618 6.503 Point 15 2.606 0.663 6.503 Point 16 2.554 0.709 6.502 Point 17 2.502 0.754 6.502 Point 18 2.450 0.800 6.501 Point 19 2.399 0.845 6.501 Point 20 2.346 0.889 6.500 Point 21 2.295 0.935 6.499 Point 22 2.241 0.979 6.499 Point 23 2.189 1.023 6.498 Point 24 2.136 1.067 6.498 Point 25 2.083 1.111 6.497 Point 26 2.030 1.154 6.497 Point 27 1.975 1.198 6.496 Point 28 1.922 1.240 6.496 Point 29 1.867 1.282 6.495 Point 30 1.813 1.324 6.495 Point 31 1.758 1.365 6.494 Point 32 1.703 1.406 6.494 Point 33 1.647 1.446 6.493 Point 34 1.590 1.486 6.493 Point 35 1.533 1.525 6.493 Point 36 1.475 1.562 6.492 Point 37 1.418 1.599 6.492 Point 38 1.359 1.636 6.491 Point 39 1.300 1.670 6.491 Point 40 1.240 1.705 6.490 Point 41 1.179 1.737 6.490 Point 42 1.118 1.767 6.490 Point 43 1.056 1.797 6.489 Point 44 0.993 1.824 6.489 Point 45 0.928 1.849 6.489 Point 46 0.863 1.871 6.488 Point 47 0.797 1.890 6.488 Point 48 0.730 1.906 6.488 Point 49 0.662 1.917 6.488 Point 50 0.593 1.924 6.488 Point 51 0.524 1.926 6.488 Point 52 0.456 1.921 6.488 Point 53 0.388 1.910 6.488 Point 54 0.322 1.892 6.488 Point 55 0.257 1.867 6.488 Point 56 0.197 1.835 6.489 Point 57 0.140 1.796 6.489 Point 58 0.088 1.751 6.490 Point 59 0.041 1.701 6.490 Point 60 0.000 1.646 6.491 Point 61 −0.035 1.586 6.492 Point 62 −0.062 1.523 6.493 Point 63 −0.079 1.456 6.493 Point 64 −0.080 1.388 6.494 Point 65 −0.060 1.323 6.495 Point 66 −0.012 1.275 6.495 Point 67 0.054 1.259 6.496 Point 68 0.119 1.280 6.495 Point 69 0.177 1.317 6.495 Point 70 0.234 1.356 6.495 Point 71 0.291 1.395 6.494 Point 72 0.349 1.430 6.494 Point 73 0.412 1.460 6.493 Point 74 0.476 1.482 6.493 Point 75 0.543 1.496 6.493 Point 76 0.612 1.503 6.493 Point 77 0.681 1.500 6.493 Point 78 0.750 1.491 6.493 Point 79 0.817 1.477 6.493 Point 80 0.883 1.458 6.493 Point 81 0.948 1.435 6.494 Point 82 1.012 1.409 6.494 Point 83 1.074 1.382 6.494 Point 84 1.136 1.352 6.495 Point 85 1.197 1.319 6.495 Point 86 1.258 1.287 6.495 Point 87 1.318 1.253 6.496 Point 88 1.377 1.218 6.496 Point 89 1.435 1.182 6.497 Point 90 1.494 1.146 6.497 Point 91 1.552 1.108 6.497 Point 92 1.610 1.071 6.498 Point 93 1.667 1.033 6.498 Point 94 1.724 0.995 6.499 Point 95 1.781 0.956 6.499 Point 96 1.837 0.917 6.500 Point 97 1.894 0.877 6.500 Point 98 1.950 0.838 6.501 Point 99 2.007 0.798 6.501 Point 100 2.063 0.759 6.502 Point 101 2.120 0.719 6.502 Point 102 2.176 0.679 6.502 Point 103 2.231 0.639 6.503 Point 104 2.287 0.599 6.503 Point 105 2.343 0.559 6.504 Point 106 2.398 0.518 6.504 Point 107 2.454 0.478 6.505 Point 108 2.510 0.438 6.505 Point 109 2.566 0.397 6.506 Point 110 2.622 0.357 6.506 Point 111 2.678 0.318 6.507 Point 112 2.734 0.277 6.507 Point 113 2.789 0.237 6.508 Point 114 2.845 0.196 6.508 Point 115 2.901 0.156 6.509 Point 116 2.957 0.116 6.509 Point 117 3.013 0.076 6.510 Point 118 3.069 0.037 6.510 Point 119 3.125 −0.004 6.510 Point 120 3.185 −0.036 6.511 Section 10 Point 1 3.180 0.001 7.441 Point 2 3.194 0.064 7.440 Point 3 3.153 0.117 7.439 Point 4 3.104 0.164 7.439 Point 5 3.055 0.210 7.438 Point 6 3.006 0.257 7.437 Point 7 2.956 0.305 7.437 Point 8 2.907 0.352 7.436 Point 9 2.858 0.398 7.436 Point 10 2.808 0.445 7.435 Point 11 2.759 0.492 7.435 Point 12 2.709 0.538 7.434 Point 13 2.660 0.583 7.434 Point 14 2.610 0.630 7.433 Point 15 2.560 0.676 7.433 Point 16 2.510 0.722 7.432 Point 17 2.459 0.767 7.431 Point 18 2.410 0.813 7.431 Point 19 2.359 0.859 7.430 Point 20 2.308 0.904 7.430 Point 21 2.257 0.948 7.429 Point 22 2.207 0.994 7.429 Point 23 2.155 1.038 7.428 Point 24 2.104 1.083 7.428 Point 25 2.053 1.127 7.427 Point 26 2.001 1.171 7.427 Point 27 1.948 1.215 7.426 Point 28 1.896 1.258 7.426 Point 29 1.843 1.301 7.425 Point 30 1.790 1.343 7.425 Point 31 1.737 1.385 7.424 Point 32 1.683 1.427 7.424 Point 33 1.629 1.469 7.423 Point 34 1.575 1.509 7.423 Point 35 1.520 1.549 7.422 Point 36 1.465 1.589 7.422 Point 37 1.410 1.627 7.421 Point 38 1.354 1.665 7.421 Point 39 1.296 1.703 7.420 Point 40 1.238 1.739 7.420 Point 41 1.180 1.774 7.420 Point 42 1.121 1.807 7.419 Point 43 1.061 1.839 7.419 Point 44 1.001 1.870 7.419 Point 45 0.939 1.898 7.418 Point 46 0.876 1.925 7.418 Point 47 0.813 1.949 7.418 Point 48 0.749 1.970 7.417 Point 49 0.682 1.987 7.417 Point 50 0.616 2.001 7.417 Point 51 0.549 2.009 7.417 Point 52 0.481 2.012 7.417 Point 53 0.413 2.010 7.417 Point 54 0.345 1.999 7.417 Point 55 0.280 1.981 7.417 Point 56 0.217 1.957 7.417 Point 57 0.157 1.925 7.418 Point 58 0.102 1.886 7.418 Point 59 0.051 1.840 7.419 Point 60 0.008 1.789 7.419 Point 61 −0.030 1.732 7.420 Point 62 −0.059 1.670 7.421 Point 63 −0.076 1.605 7.422 Point 64 −0.076 1.537 7.422 Point 65 −0.050 1.475 7.423 Point 66 0.002 1.432 7.424 Point 67 0.068 1.424 7.424 Point 68 0.132 1.447 7.423 Point 69 0.190 1.480 7.423 Point 70 0.248 1.517 7.423 Point 71 0.307 1.549 7.422 Point 72 0.369 1.577 7.422 Point 73 0.435 1.597 7.422 Point 74 0.501 1.609 7.422 Point 75 0.569 1.612 7.422 Point 76 0.637 1.606 7.422 Point 77 0.704 1.594 7.422 Point 78 0.769 1.576 7.422 Point 79 0.833 1.555 7.422 Point 80 0.897 1.529 7.423 Point 81 0.958 1.501 7.423 Point 82 1.018 1.470 7.423 Point 83 1.079 1.438 7.424 Point 84 1.138 1.404 7.424 Point 85 1.196 1.369 7.424 Point 86 1.253 1.333 7.425 Point 87 1.311 1.297 7.425 Point 88 1.368 1.259 7.426 Point 89 1.424 1.221 7.426 Point 90 1.480 1.183 7.427 Point 91 1.535 1.144 7.427 Point 92 1.591 1.104 7.428 Point 93 1.646 1.065 7.428 Point 94 1.701 1.025 7.428 Point 95 1.756 0.985 7.429 Point 96 1.811 0.945 7.429 Point 97 1.865 0.905 7.430 Point 98 1.920 0.864 7.430 Point 99 1.974 0.824 7.431 Point 100 2.028 0.783 7.431 Point 101 2.083 0.742 7.432 Point 102 2.138 0.701 7.432 Point 103 2.191 0.661 7.433 Point 104 2.245 0.620 7.433 Point 105 2.300 0.578 7.434 Point 106 2.354 0.537 7.434 Point 107 2.408 0.496 7.435 Point 108 2.462 0.455 7.435 Point 109 2.516 0.414 7.436 Point 110 2.571 0.373 7.436 Point 111 2.625 0.333 7.437 Point 112 2.679 0.292 7.437 Point 113 2.733 0.251 7.438 Point 114 2.788 0.210 7.438 Point 115 2.842 0.170 7.439 Point 116 2.896 0.129 7.439 Point 117 2.951 0.088 7.439 Point 118 3.005 0.048 7.440 Point 119 3.060 0.007 7.440 Point 120 3.119 −0.024 7.441 Section 11 Point 1 3.109 0.017 8.370 Point 2 3.125 0.080 8.370 Point 3 3.087 0.134 8.369 Point 4 3.039 0.181 8.368 Point 5 2.992 0.229 8.368 Point 6 2.944 0.276 8.367 Point 7 2.896 0.323 8.367 Point 8 2.847 0.370 8.366 Point 9 2.799 0.418 8.366 Point 10 2.751 0.465 8.365 Point 11 2.703 0.511 8.365 Point 12 2.655 0.558 8.364 Point 13 2.607 0.605 8.363 Point 14 2.558 0.651 8.363 Point 15 2.509 0.698 8.362 Point 16 2.461 0.744 8.362 Point 17 2.412 0.791 8.361 Point 18 2.363 0.837 8.361 Point 19 2.314 0.882 8.360 Point 20 2.265 0.928 8.360 Point 21 2.215 0.973 8.359 Point 22 2.166 1.019 8.359 Point 23 2.116 1.064 8.358 Point 24 2.066 1.109 8.358 Point 25 2.016 1.155 8.357 Point 26 1.965 1.198 8.356 Point 27 1.915 1.243 8.356 Point 28 1.864 1.287 8.355 Point 29 1.813 1.331 8.355 Point 30 1.762 1.375 8.354 Point 31 1.710 1.418 8.354 Point 32 1.658 1.460 8.353 Point 33 1.607 1.502 8.353 Point 34 1.553 1.544 8.352 Point 35 1.501 1.586 8.352 Point 36 1.447 1.627 8.351 Point 37 1.393 1.667 8.351 Point 38 1.339 1.706 8.351 Point 39 1.284 1.744 8.350 Point 40 1.229 1.783 8.350 Point 41 1.172 1.820 8.349 Point 42 1.115 1.856 8.349 Point 43 1.058 1.890 8.348 Point 44 0.999 1.924 8.348 Point 45 0.940 1.955 8.348 Point 46 0.880 1.986 8.347 Point 47 0.819 2.013 8.347 Point 48 0.756 2.039 8.347 Point 49 0.693 2.061 8.346 Point 50 0.628 2.080 8.346 Point 51 0.563 2.095 8.346 Point 52 0.496 2.105 8.346 Point 53 0.429 2.109 8.346 Point 54 0.362 2.106 8.346 Point 55 0.296 2.097 8.346 Point 56 0.231 2.080 8.346 Point 57 0.168 2.056 8.346 Point 58 0.110 2.022 8.347 Point 59 0.056 1.981 8.347 Point 60 0.009 1.933 8.348 Point 61 −0.031 1.879 8.348 Point 62 −0.061 1.819 8.349 Point 63 −0.077 1.754 8.350 Point 64 −0.073 1.688 8.351 Point 65 −0.040 1.630 8.351 Point 66 0.016 1.593 8.352 Point 67 0.082 1.594 8.352 Point 68 0.144 1.621 8.352 Point 69 0.203 1.653 8.351 Point 70 0.262 1.686 8.351 Point 71 0.323 1.712 8.350 Point 72 0.387 1.730 8.350 Point 73 0.454 1.739 8.350 Point 74 0.521 1.738 8.350 Point 75 0.588 1.728 8.350 Point 76 0.653 1.711 8.350 Point 77 0.717 1.689 8.351 Point 78 0.778 1.664 8.351 Point 79 0.839 1.634 8.351 Point 80 0.899 1.602 8.352 Point 81 0.957 1.570 8.352 Point 82 1.015 1.535 8.353 Point 83 1.071 1.499 8.353 Point 84 1.128 1.461 8.353 Point 85 1.182 1.424 8.354 Point 86 1.238 1.385 8.354 Point 87 1.293 1.346 8.355 Point 88 1.347 1.307 8.355 Point 89 1.401 1.267 8.356 Point 90 1.455 1.226 8.356 Point 91 1.509 1.186 8.357 Point 92 1.563 1.145 8.357 Point 93 1.616 1.105 8.358 Point 94 1.669 1.063 8.358 Point 95 1.722 1.022 8.359 Point 96 1.775 0.981 8.359 Point 97 1.828 0.939 8.360 Point 98 1.880 0.897 8.360 Point 99 1.934 0.856 8.361 Point 100 1.987 0.814 8.361 Point 101 2.039 0.773 8.361 Point 102 2.092 0.732 8.362 Point 103 2.144 0.690 8.362 Point 104 2.197 0.648 8.363 Point 105 2.250 0.606 8.363 Point 106 2.302 0.564 8.364 Point 107 2.356 0.523 8.364 Point 108 2.408 0.481 8.365 Point 109 2.461 0.439 8.365 Point 110 2.514 0.397 8.366 Point 111 2.567 0.356 8.366 Point 112 2.620 0.314 8.367 Point 113 2.672 0.273 8.367 Point 114 2.725 0.232 8.368 Point 115 2.778 0.190 8.368 Point 116 2.832 0.148 8.369 Point 117 2.885 0.108 8.369 Point 118 2.938 0.066 8.370 Point 119 2.991 0.025 8.370 Point 120 3.048 −0.006 8.371 Section 12 Point 1 3.035 0.040 9.300 Point 2 3.053 0.102 9.299 Point 3 3.017 0.156 9.299 Point 4 2.971 0.204 9.298 Point 5 2.925 0.252 9.298 Point 6 2.878 0.300 9.297 Point 7 2.832 0.348 9.297 Point 8 2.785 0.394 9.296 Point 9 2.739 0.442 9.295 Point 10 2.692 0.490 9.295 Point 11 2.644 0.538 9.294 Point 12 2.598 0.584 9.294 Point 13 2.550 0.632 9.293 Point 14 2.504 0.679 9.293 Point 15 2.456 0.726 9.292 Point 16 2.409 0.773 9.292 Point 17 2.362 0.819 9.291 Point 18 2.314 0.867 9.290 Point 19 2.266 0.913 9.290 Point 20 2.218 0.959 9.289 Point 21 2.170 1.005 9.289 Point 22 2.122 1.051 9.288 Point 23 2.073 1.097 9.288 Point 24 2.025 1.143 9.287 Point 25 1.976 1.188 9.287 Point 26 1.928 1.234 9.286 Point 27 1.879 1.278 9.286 Point 28 1.829 1.324 9.285 Point 29 1.780 1.368 9.285 Point 30 1.730 1.412 9.284 Point 31 1.680 1.457 9.284 Point 32 1.629 1.500 9.283 Point 33 1.578 1.543 9.282 Point 34 1.528 1.586 9.282 Point 35 1.476 1.629 9.281 Point 36 1.425 1.671 9.281 Point 37 1.373 1.713 9.280 Point 38 1.320 1.753 9.280 Point 39 1.266 1.793 9.280 Point 40 1.213 1.833 9.279 Point 41 1.159 1.872 9.279 Point 42 1.104 1.909 9.278 Point 43 1.048 1.946 9.278 Point 44 0.992 1.982 9.277 Point 45 0.935 2.016 9.277 Point 46 0.878 2.049 9.277 Point 47 0.818 2.080 9.276 Point 48 0.758 2.110 9.276 Point 49 0.697 2.136 9.276 Point 50 0.635 2.160 9.275 Point 51 0.572 2.180 9.275 Point 52 0.507 2.197 9.275 Point 53 0.441 2.208 9.275 Point 54 0.374 2.213 9.275 Point 55 0.308 2.211 9.275 Point 56 0.243 2.202 9.275 Point 57 0.178 2.184 9.275 Point 58 0.117 2.157 9.275 Point 59 0.060 2.122 9.276 Point 60 0.010 2.079 9.276 Point 61 −0.033 2.029 9.277 Point 62 −0.066 1.970 9.277 Point 63 −0.080 1.906 9.278 Point 64 −0.069 1.841 9.279 Point 65 −0.028 1.789 9.280 Point 66 0.031 1.761 9.280 Point 67 0.097 1.769 9.280 Point 68 0.157 1.796 9.280 Point 69 0.217 1.826 9.279 Point 70 0.279 1.852 9.279 Point 71 0.342 1.870 9.279 Point 72 0.409 1.878 9.279 Point 73 0.475 1.874 9.279 Point 74 0.541 1.860 9.279 Point 75 0.604 1.840 9.279 Point 76 0.665 1.813 9.279 Point 77 0.725 1.783 9.280 Point 78 0.783 1.750 9.280 Point 79 0.839 1.716 9.280 Point 80 0.895 1.679 9.281 Point 81 0.950 1.641 9.281 Point 82 1.005 1.603 9.282 Point 83 1.058 1.563 9.282 Point 84 1.112 1.524 9.283 Point 85 1.164 1.484 9.283 Point 86 1.217 1.443 9.284 Point 87 1.270 1.401 9.284 Point 88 1.322 1.360 9.285 Point 89 1.374 1.318 9.285 Point 90 1.426 1.276 9.286 Point 91 1.477 1.234 9.286 Point 92 1.529 1.192 9.287 Point 93 1.581 1.150 9.287 Point 94 1.632 1.108 9.288 Point 95 1.684 1.065 9.288 Point 96 1.734 1.023 9.289 Point 97 1.786 0.980 9.289 Point 98 1.838 0.937 9.290 Point 99 1.889 0.895 9.290 Point 100 1.940 0.852 9.291 Point 101 1.991 0.809 9.291 Point 102 2.042 0.767 9.292 Point 103 2.094 0.725 9.292 Point 104 2.145 0.682 9.293 Point 105 2.196 0.639 9.293 Point 106 2.248 0.596 9.294 Point 107 2.299 0.554 9.294 Point 108 2.350 0.511 9.295 Point 109 2.402 0.469 9.295 Point 110 2.453 0.427 9.296 Point 111 2.505 0.384 9.296 Point 112 2.556 0.342 9.297 Point 113 2.608 0.300 9.297 Point 114 2.659 0.257 9.298 Point 115 2.710 0.215 9.298 Point 116 2.762 0.174 9.299 Point 117 2.814 0.131 9.299 Point 118 2.865 0.089 9.300 Point 119 2.918 0.047 9.300 Point 120 2.975 0.016 9.300

FIG. 6 illustrates an airfoil shape including a thinned outboard section 1380 according to an exemplary embodiment. The turbine blades may include blade shroud segments in order to control and minimize leakage flow between the blade tips and the surrounding stator as well as to limit vibration amplitudes. A blade shroud segment can include a platform extending in a plane parallel to the stator opposite to the blade tip. The platform of a blade shroud segment can be shaped such that its edges are parallel to those of an adjacent blade shroud platform. The shroud lifetime can be limited by mechanical stresses caused by centrifugal forces. Such stresses can be reduced by minimizing a wall thickness of the platform. However, a blade shroud segment with a thin wall thickness may not line up with the blade shroud segment of an adjacent blade due to manufacturing and assembly tolerances. A further mismatch can result from deformations of the shroud platform during turbine operation due to thermal and mechanical loading. The shroud can be designed with materials having a creep resistance. In order to improve vibrational characteristics, to improve creep resistance, and to improve blade loading, a newly designed airfoil shape is needed. According to the newly designed airfoil shape of the exemplary embodiment which includes a thinned outboard section 1380 as illustrated in FIG. 6, it is possible to improve vibrational characteristics, to improve creep resistance, and to improve blade loading. Further, the airfoil configuration according to the exemplary embodiment which includes an increased chord near the hub improves vibrational characteristics, creep resistance and blade loading.

While one or more exemplary embodiments have been described with reference to the accompanying drawings, it is to be understood by those skilled in the art that various modifications and changes in form and details can be made therein without departing from the spirit and scope as defined by the appended claims. Therefore, the description of the exemplary embodiments should be construed in a descriptive sense only and not to limit the scope of the claims, and many alternatives, modifications, and variations will be apparent to those skilled in the art. 

What is claimed is:
 1. A turbine blade comprising: an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.
 2. The turbine blade according to claim 1, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 3. The turbine blade according to claim 1, wherein the airfoil shape lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 4. The turbine blade according to claim 1, wherein the airfoil shape lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 5. The turbine blade according to claim 1, wherein a height of the airfoil portion is approximately 9 to 11 inches.
 6. The turbine blade according to claim 1, wherein a height of the turbine blade is approximately 16 to 18 inches.
 7. The turbine blade according to claim 1, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.
 8. A turbine comprising: a rotor disk configured to be rotatable; and a plurality of turbine blades installed on the rotor disk, wherein each of the turbine blade comprises an airfoil having a blade-shape extending from a platform to a tip shroud and including a leading edge, a trailing edge, a pressure side extending from the leading edge to the trailing edge, and a suction side extending from the leading edge to the trailing edge, wherein the turbine blade comprises an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.
 9. The turbine according to claim 8, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 10. The turbine according to claim 8, wherein the airfoil shape lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 11. The turbine according to claim 8, wherein the airfoil shape lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 12. The turbine according to claim 8, wherein a height of the airfoil portion is approximately 9 to 11 inches.
 13. The turbine according to claim 8, wherein a height of the turbine blade is approximately 16 to 18 inches.
 14. The turbine according to claim 8, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.
 15. A gas turbine comprising: a compressor configured to compress air; a combustor configured to mix compressed air supplied from the compressor with fuel for combustion to generate combustion gas; and a turbine comprising a plurality of turbine nozzles and a plurality of turbine blades rotated by the combustion gas to generate power, wherein each of the turbine blades extending from a platform to a tip shroud and having an airfoil-shaped cross section and including a leading edge, a trailing edge, a pressure side extending from the leading edge to the trailing edge, and a suction side extending from the leading edge to the trailing edge, wherein the turbine blade comprises an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.
 16. The gas turbine according to claim 15, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 17. The gas turbine according to claim 15, wherein the airfoil shape lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 18. The gas turbine according to claim 15, The turbine nozzle according to claim 1, wherein the airfoil shape lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.
 19. The gas turbine according to claim 15, wherein a height of the airfoil portion is approximately 9 to 11 inches.
 20. The gas turbine according to claim 15, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches. 